643edo: Difference between revisions
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{{EDO intro|643}} | |||
only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it [[support]]s [[ | |||
643edo is uniquely [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament. | |||
643edo is the 117th [[prime edo]]. | 643edo is the 117th [[prime edo]]. | ||
{{Harmonics in equal|643|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 20:34, 29 August 2022
643edo is uniquely consistent to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log25, after 146 and before 4004. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it supports the sesquiquartififths temperament. In the 11-limit it tempers out 3025/3024 and 151263/151250; in the 13-limit 1001/1000, 1716/1715 and 4225/4224; in the 17-limit 1089/1088, 1701/1700, 2431/2430 and 2601/2600; and in the 19-limit 1331/1330, 1521/1520, 1729/1728, 2376/2375 and 2926/2925. It provides the optimal patent val for the rank-3 13-limit vili temperament.
643edo is the 117th prime edo.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.244 | +0.000 | -0.241 | -0.774 | -0.714 | -0.445 | -0.779 | +0.653 | +0.594 | +0.843 |
| Relative (%) | +0.0 | -13.1 | +0.0 | -12.9 | -41.5 | -38.3 | -23.9 | -41.7 | +35.0 | +31.8 | +45.2 | |
| Steps (reduced) |
643 (0) |
1019 (376) |
1493 (207) |
1805 (519) |
2224 (295) |
2379 (450) |
2628 (56) |
2731 (159) |
2909 (337) |
3124 (552) |
3186 (614) | |